You may remember that I collect slide rules. If you don’t, it probably doesn’t surprise you. I have a large number of what I think of as normal slide rules. I also have the less common circular and cylindrical slide rules. But I recently picked up a real oddity that I had to share: the Smarty Cat. It isn’t exactly a slide rule but it sort of is if you stretch the definition a bit.
Real Slide Rules
A regular slide rule takes advantage of the fact that you can multiply and divide by adding logarithms. Imagine having two rulers marked in inches or centimeters — it doesn’t matter (see the adjoining image). Suppose you want to add 5 and 3. You count off 5 marks on one ruler and line it with up the zero inch mark on the other ruler. Now you count off 3 marks on the second ruler and that position on the first ruler will indicate the result. Here it lines up with the 8 mark, which is, of course, the correct answer.
That’s a simple addition. But if you can convert your numbers into logarithms, add the logarithms, and then back out to a regular number, you can multiply.
Logarithms and Slide Rules
Let’s try a multiplication example: 10 times 100. Using base 10 logarithms, the marks on the ruler will be 1 and 2 (because 101=10 and 102=100). If you add 1 and 2 you get 3 and 103 is, in fact, 1000 which is the right answer. That’s how a normal slide rule works. There’s a cursor (a clear plastic slide) that rides over the rulers so you can precisely tell where the rules line up.
Look at the scales on the rule in the picture. See the 1 on the C scale? That’s the same as zero in the simple illustration above because 100=1. It lines up to 1.5 on the D scale (or 15, or 150; they are all the same). Now look under the crosshair on the cursor. The 2 on the C scale lines up with the 3 on the D scale. That means that 1.5 x 2=3. It also means 1.5 x 20=30, 15 x 2.0=30, and 15 x 20 = 300, among other things. There’s nothing magic about the cursor. If you look a bit to the right, you can see that 1.5 x 1.3=1.95, and 15 x 1.3=19.5.
Smarty Cat
The Smarty Cat is very different, yet it can add, subtract, multiply, and divide small integers. The Cat is more like a single ruler with three scales on each side of the ruler. None of these scales ever move. However, there is a cursor that appears like a cat’s face — it isn’t transparent, but there are holes for the cat’s eyes and nose. The scales are such that when two numbers show up in the eyes, the number under the cat’s nose will be the sum of the other two numbers. It also means that the number under the nose minus one of the eye numbers will equal the other eye number. The photo shows 7 + 3 = 10, for example.
The other side of the rule has a different arrangement of numbers. On that side, the two eye numbers multiplied together give you the number under the nose. By the same token, the nose number divided by either eye number will result in the other eye number. That is if you look in the photograph, 7 x 4 = 28. Of course, 28/7=4 and 28/4=7.
Calculator
By today’s standards, this isn’t much of a calculator. Still, it is pretty ingenious how people figured out ways to automate math before we had computers. While I’ll admit it isn’t really a slide rule in the classic sense, it is still a pretty fun collectible.
I’ve talked about regular slide rules before. I’ve even argued that the death of the slide rule has hurt the quality of engineering graduates. We’d love to hear your thoughts, and see some of the more interesting slide rules you have in your collection, in the comments below.
Maybe Smarty Cat is a form of nomogramand the “cursor” is a way to line up related values from 3 different curves.
That was my first thought too.
https://en.wikipedia.org/wiki/Nomogram
Not really, it’s just an offset table.
Mechanical lookup table
It IS very cute – too bad you didn’t think of it 70 years ago, I’m sure that it would have sold well!
Well, the patent goes back to 1953, although I don’t know how well they sold.
Mostly because I had to learn my times tables up to 12 x 12 and this appear not to go that high (maybe on the other side?)
One side is addition/subtraction and the other side is multiplication/division.
I still have my “Snoopy” slide rule from the 70’s. Just like this one:
https://www.sliderulemuseum.com/MiscUSA/S534_Snoopy_SR_1965UnitedFeatureSyndicate.jpg
I want to see someone build a digital slide rule. Digital calipers could be a starting point. Why? Because if Hal Clement’s book “Mission of Gravity” ever gets made into a movie it’d be a way to keep the slide rules it often mentions some characters using.
Don’t really want it digital all the way through. Analog computing is more compatible. You’d want to just output digitally through an ADC … or if you really insist … pull a sneaky and use a digital CMOS inverter as op-amps and do the same… or if you really, really insist… sigh and dig out that TI calculator chip with the good logarithm support…
For that, movie props are sufficient. :-) I’m not sure, if the digital calipers have more transistors than the first pocket calculators anyway. :-)
But some people like “useless machines” or suffer from nostalgia. :-)
Al, you may be interested in that circular one i made then: https://www.bjonnh.net/article/20170530_cccslider/
Wow. Excellent work!
Nice! The animation is very cool. I have a nice yellow Pickett circular with the two cursors. I use it occasionally.
very cool!
I remember having something like this with a Mickey Mouse theme when I was younger.
What age range of toddler is this intended for? It’s a lookup table, not a slide rule. I regret no longer having my slide rule (I think it was a Christmas gift) and I wish they would come back. Sadly that’s not gonna happen.
From three to about 8 or 9 for boys. Three to 6 for girls as they typically develop the cognitive skills for learning the multiplication tables much earlier. Ebay has tons of good rules available.
Working with a Slide Rule daily in the days before the SR calcs gave everybody, well almost everybody, an intuitive feel for the outcome of some pretty tricky math often without even using one. A quick dirty answer often led to insights that wouldn’t have happened otherwise. This does seem to be lacking in the 21st century. Yes, I am an old guy.
39 years old, and I just recently saw my first slide rule in person. As luck would have it, at a local thrift store, so now I finally have a slide rule, unfortunately, it’s a specialized one for radio (iirc).
If that’s really a two-sided radio model, then it’s probably rarer and more valuable than most other slide rules. Look it up at the online Slide Rule Museum.
I am nearly 49, but I never had to use a slide rule – though my father once showed me some, he used at university. But at the time he showed me the old slide rules we already had pocket calculators. He showed it to me just as a curiosity. I still have his first HP pocket calculator – with red LED display and quite power hungry. So it has a “wall wart” PSU which entirely relied on the NiCd batteries to smooth the power. I should replace the corroded battery contacts with some Ni strip to be able to use it again.
My mum used to boast of being faster with log tables than her classmates were with a slide rule – and obviously more accurate too.
One snide comment about me being faster and more accurate with a calculator, and my calculator was confiscated, and I had to bring a slide rule and log tables to school for maths (GCSE).
Maybe someone will post CNC plans on how to make your own. If I ever get a CNC machine I would make some as gifts to some kids I know.
I saw this as a kid in the 1970’s. My dad’s friend had a company that was selling them so I got one free. It was just a calculator for kids to do simple maths on.
No idea whatever happened to the company that was selling them, but it had the odd name of ‘Gayton Impex’ and that, with the memory of my smarty cat rule is what brought me here…